Spinning Brownian motion

被引：0

作者：

Duarte, Mauricio A. ^{[1
]}

机构：

[1] Univ Andres Bello, Dept Matemat, Santiago, Chile

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 11期

基金：

美国国家科学基金会;

关键词：

Stationary distribution; Stochastic differential equations; Excursion theory; Degenerate reflected diffusion; STOCHASTIC DIFFERENTIAL-EQUATIONS; STATIONARY DISTRIBUTIONS; BOUNDARY-CONDITIONS; OBLIQUE REFLECTION; DOMAINS;

D O I：

10.1016/j.spa.2015.06.005

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove strong existence and uniqueness for a reflection process X in a smooth, bounded domain D that behaves like obliquely-reflected-Brownian-motion, except that the direction of reflection depends on a (spin) parameter S, which only changes when X is on the boundary of D according to a physical rule. The process (X, S) is a degenerate diffusion. We show uniqueness of the stationary distribution by using techniques based on excursions of X from partial derivative D, and an associated exit system. We also show that the process admits a submartingale formulation and use related results to show examples of the stationary distribution. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：4178 / 4203

页数：26

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